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We survey some of the recent advances in mean estimation and regression function estimation.
Probability inequalities for sums of bounded random variables
W. Hoeffding · 1963
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Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/winsorization 1
J.W. Tukey and D.H. McLaughlin · 1963
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Robust estimation of a location parameter
P.J. Huber · 1964
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On some robust estimates of location
P.J. Bickel · 1965
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The asymptotic distribution of the trimmed mean
S.M. Stigler · 1973
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Mathematics and the picturing of data
J.W. Tukey · 1975
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Norm of Gaussian sample function
B.S. Tsirelson, I.A. Ibragimov, and V.N. Sudakov · 1976
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Theory of Pattern Recognition
V.N. Vapnik and A.Ya. Chervonenkis · 1979
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Problem complexity and method efficiency in optimization
A.S. Nemirovsky and D.B. Yudin · 1983
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A theory of the learnable
L.G. Valiant · 1984
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Robust statistics: the approach based on influence functions
F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel · 1986
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Random generation of combinatorial structures from a uniform distribution
M. Jerrum, L. Valiant, and V. Vazirani · 1986
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Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M.K. Warmuth · 1989
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A survey of multidimensional medians
C.G. Small · 1990
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Probability in Banach Space
M. Ledoux and M. Talagrand · 1991
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Limit theorems of probability theory: sequences of independent random variables
Valentin V Petrov · 1995
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A Probabilistic Theory of Pattern Recognition
L. Devroye, L. Györfi, and G. Lugosi · 1996
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Weak convergence and empirical processes
A.W. van der Waart and J.A. Wellner · 1996
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Neural Network Learning: Theoretical Foundations
M. Anthony and P. L. Bartlett · 1999
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Applications of empirical process theory
S. van de Geer · 2000
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The concentration of measure phenomenon
M. Ledoux · 2001
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The space complexity of approximating the frequency moments
N. Alon, Y. Matias, and M. Szegedy · 2002
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A distribution-free theory of nonparametric regression
L. Györfi, M. Kohler, A. Krzyżak, and H. Walk · 2002
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Localized Rademacher complexities
P.L. Bartlett, O. Bousquet, and S. Mendelson · 2005
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Geometric measures of data depth
G. Aloupis · 2006
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Concentration inequalities and model selection
P. Massart · 2006
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Oracle inequalities in empirical risk minimization and sparse recovery problems
V. Koltchinskii · 2008
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Robust statistics
P.J. Huber and E.M. Ronchetti · 2009
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Introduction to nonparametric estimation
A. B. Tsybakov · 2009
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Lectures in geometric functional analysis
R. Vershynin · 2009
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Robust statistics
D. Hsu · 2010
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Robust linear least squares regression
J.-Y. Audibert and O. Catoni · 2011
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Statistics for high-dimensional data
P. Bühlmann and S. van de Geer · 2011
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Challenging the empirical mean and empirical variance: a deviation study
O. Catoni · 2012
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On the estimation of the mean of a random vector
E. Joly, G. Lugosi, and R. I. Oliveira · 2017
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Learning from mom’s principles: Le cam’s approach
G. Lecué and M. Lerasle · 2017
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An optimal unrestricted learning procedure
S. Mendelson · 2017
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Distributed statistical estimation and rates of convergence in normal approximation
Stanislav Minsker and Nate Strawn · 2017
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Rho-estimators revisited: General theory and applications
Y. Baraud and L. Birgé · 2018
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M. Lerasle and R. I. Oliveira · 2012
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Concentration inequalities:A Nonasymptotic Theory of Independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Bandits with heavy tail
S. Bubeck, N. Cesa-Bianchi, and G. Lugosi · 2013
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A robust, adaptive m-estimator for pointwise estimation in heteroscedastic regression
M. Chichignoud and J. Lederer · 2014
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On the absolute constants in the Berry-Esseen-type inequalities
IG Shevtsova · 2014
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Empirical risk minimization for heavy-tailed losses
C. Brownlees, E. Joly, and G. Lugosi · 2015
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O. Catoni and I. Giulini · 2018
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Robustly learning a gaussian: Getting optimal error, efficiently
I. Diakonikolas, G. Kamath, D.M. Kane, J. Li, A. Moitra, and A. Stewart · 2018
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Efficient algorithms and lower bounds for robust linear regression
I. Diakonikolas, W. Kong, and A. Stewart · 2018
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Mixture models, robustness, and sum of squares proofs
S.B. Hopkins and J. Li · 2018
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Efficient algorithms for outlier-robust regression
A. Klivans, P.K. Kothari, and R. Meka · 2018
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Robust moment estimation and improved clustering via sum of squares
P.K. Kothari, J. Steinhardt, and D. Steurer · 2018
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Robust classification via mom minimization
G. Lecué, M. Lerasle, and T. Mathieu · 2018
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High-dimensional robust precision matrix estimation: Cellwise corruption under ϵ \epsilon -contamination
Po-Ling Loh and Xin Lu Tan · 2018
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Learning without concentration for general loss functions
S. Mendelson · 2018
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Robust covariance estimation under L 4 − L 2 {L}_{4}-{L}_{2} norm equivalence
S. Mendelson and N. Zhivotovskiy · 2018
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Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries
Stanislav Minsker · 2018
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Uniform bounds for robust mean estimators
Stanislav Minsker · 2018
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Fast mean estimation with sub-gaussian rates
Y. Cherapanamjeri, N. Flammarion, and P. Bartlett · 2019
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Sub-gaussian mean estimation in polynomial time
S.B. Hopkins · 2019
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An optimal ( ϵ \epsilon , δ \delta )-randomized approximation scheme for the mean of random variables with bounded relative variance
M. Huber · 2019
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Robust machine learning by median-of-means: theory and practice
G. Lecué and M. Lerasle · 2019
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Robust multivariate mean estimation: the optimality of trimmed mean
G. Lugosi and S. Mendelson · 2019
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Sub-Gaussian estimators of the mean of a random vector
G. Lugosi and S. Mendelson · 2019
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Near-optimal mean estimators with respect to general norms
G. Lugosi and S. Mendelson · 2019
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Regularization, sparse recovery, and median-of-means tournaments
G. Lugosi and S. Mendelson · 2019
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Risk minimization by median-of-means tournaments
G. Lugosi and S. Mendelson · 2019
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The sub-gaussian property of trimmed means estimators
Roberto I. Oliveira and Paulo Orenstein · 2019
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